Part 2. Notebook for Network and Topological Analysis in Neuroscience

Authors: Eduarda Centeno & Fernando Santos

This second part of the project will focus on the 3D visualisations we have developed.

Table of contents

1. Imports
2. Short recap - importing data & creating graph object
3. Creating 3D visualisations with Plotly
4. Acknowledgements

1. Imports

# Basic data manipulation and visualisation libraries
import numpy as np
import matplotlib.pyplot as plt

# Network Libraries
import networkx as nx

# Magic command to load watermark
%load_ext watermark

# Print watermark
%watermark --author "Eduarda & Fernando" --date --time --python --machine --iversion --watermark --packages jupyterlab,notebook

Author: Eduarda & Fernando

Python implementation: CPython
Python version       : 3.7.8
IPython version      : 7.18.1

jupyterlab: 1.2.0
notebook  : 6.1.4

Compiler    : MSC v.1916 64 bit (AMD64)
OS          : Windows
Release     : 10
Machine     : AMD64
Processor   : Intel64 Family 6 Model 142 Stepping 10, GenuineIntel
CPU cores   : 8
Architecture: 64bit

numpy     : 1.18.5
matplotlib: 3.3.2
meshio    : 4.0.16
networkx  : 2.4
pandas    : 1.1.3
community : 0.13
plotly    : 4.6.0

Watermark: 2.1.0

2. Short recap - importing data & creating graph object

# Import matrix
matrix = np.genfromtxt('./1000_Functional_Connectomes/Connectivity matrices/AveragedMatrix.txt')

# Absolutise for further user
matrix = abs(matrix)

# Creating Graph
G = nx.from_numpy_matrix(matrix)

# Removing self-loops
G.remove_edges_from(list(nx.selfloop_edges(G)))

# This function accepts a argument 'distance' that, in correlation-based networks, must be seen as the inverse ... 
# ... of the weight value. Thus, a high correlation value (e.g. 0.8) means a shorter distance (i.e 0.2).
G_distance_dict = {(e1, e2): 1 / abs(weight) for e1, e2, weight in G.edges(data='weight')}

# Then add them as attributes to the graph
nx.set_edge_attributes(G, G_distance_dict, 'distance')

# Create graphs from comparison
matrix2 = matrix.copy()
matrix3 = matrix.copy()

# Create sparser graphs
matrix2[matrix2<=0.50] = 0
matrix3[matrix3<=0.75] = 0

st50G = nx.from_numpy_matrix(matrix2)
st25G = nx.from_numpy_matrix(matrix3)

st50G.remove_edges_from(list(nx.selfloop_edges(st50G)))
st25G.remove_edges_from(list(nx.selfloop_edges(st25G)))

3. Creating 3D visualisations with Plotly

First, we need to import the necessary backup script. Then, it is possible to use a list of values for most of the nodal metrics, e.g., centralities, etc.

%run "./Background Scripts/HCP_Data_Vis.py"

Let's start with the visualisation of pairwise interactions

# Create list of values for a property
values = listnet(nx.closeness_centrality, G, distance='distance')

## Visualisation of nodes according to proprieties
# This function will plot the 3D brain with both node size and color according to node_prop
Plot_Brain_Prop(node_prop=values, scale=5) # the second parameter is necessary to scale the node size

## It is also possible to give a second property, which will change the color of the nodes

# Create a list of a second property
values_2 = listnet(nx.eigenvector_centrality, G, weight='weight')

# Plot 3D brain with node size accoring to values and node colors according to values_2
Plot_Brain_Prop(node_prop=values, scale=5, node_colors=values_2)

# We have created a degree-specific function for 3D network plotting. 
# Node size will always represent the degree/strength, node color can be changed.

# Plotting with both size and colors according to degree (or strength if weight is True)
degree_3D(st50G, scale=0.2, weight=True)

# Plotting with size according to degree/strength and colors according another property
degree_3D(st50G, scale=0.2, weight=True, node_colors=values, color_prop_name='Closeness Centrality')

# Visualisation of brain modularity
Plot_Brain_Mod(G, scale=0.75)

# Visualisation of brain network Participation Rank
thr_value = 0.5 # for plot title
clique_size = 2 # this is a line
alpha = 0.1
plotclique3dk(st50G, thr_value, clique_size, alpha) # we will use the st50G to allow a better/clearer visualisation

Let's now have a look at high-dimensional interactions (TDA)

# Visualisation of triangles (or 3-cliques)
thr_value = 0.5 # for plot title
clique_size = 3 # this is a triangle
alpha = 0.1
plotclique3dk(st50G, thr_value, clique_size, alpha)

# Visualisation of tetrahedrons (or 4-cliques)
thr_value = 0.5 # for plot title
clique_size = 4 # this is a terahedron
alpha = 0.1
plotclique3dk(st50G, thr_value, clique_size, alpha)

# Visualisation of Nodal Curvature
thr_value = 0.5 # for plot title
plotcurv(st50G, thr_value)

4. Acknowledgements

The 1000_Functional_Connectomes dataset was downloaded from the The UCLA multimodal connectivity database.